# Layer-Parallel Training for Transformers

arXiv: https://arxiv.org/abs/2601.09026 · HTML: https://mlsanity.com/paper/2601.09026/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 57 references that are in the map.
- First posted on arXiv 13 Jan 2026.

## Builds on (most cited first, 30 of 30)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [mT5: A massively multilingual pre-trained text-to-text transformer](https://mlsanity.com/paper/2010.11934/) (2020)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [Efficient Large-Scale Language Model Training on GPU Clusters Using Megatron-LM](https://mlsanity.com/paper/2104.04473/) (2021)
- [A Comprehensive Survey on Pretrained Foundation Models: A History from BERT to ChatGPT](https://mlsanity.com/paper/2302.09419/) (2023)
- [Stable Architectures for Deep Neural Networks](https://mlsanity.com/paper/1705.03341/) (2017)
- [Reducing Activation Recomputation in Large Transformer Models](https://mlsanity.com/paper/2205.05198/) (2022)
- [Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations](https://mlsanity.com/paper/1710.10121/) (2017)
- [Marian: Fast Neural Machine Translation in C++](https://mlsanity.com/paper/1804.00344/) (2018)
- [DeepNet: Scaling Transformers to 1,000 Layers](https://mlsanity.com/paper/2203.00555/) (2022)
- [Demystifying Parallel and Distributed Deep Learning: An In-Depth Concurrency Analysis](https://mlsanity.com/paper/1802.09941/) (2018)
- [TeraPipe: Token-Level Pipeline Parallelism for Training Large-Scale Language Models](https://mlsanity.com/paper/2102.07988/) (2021)
- [A Guide Through the Zoo of Biased SGD](https://mlsanity.com/paper/2305.16296/) (2023)
- [Layer-Parallel Training of Deep Residual Neural Networks](https://mlsanity.com/paper/1812.04352/) (2018)
- [On Optimizing the Communication of Model Parallelism](https://mlsanity.com/paper/2211.05322/) (2022)
- [Stateful ODE-Nets using Basis Function Expansions](https://mlsanity.com/paper/2106.10820/) (2021)
- [ODE Transformer: An Ordinary Differential Equation-Inspired Model for Neural Machine Translation](https://mlsanity.com/paper/2104.02308/) (2021)
- [DeepPCR: Parallelizing Sequential Operations in Neural Networks](https://mlsanity.com/paper/2309.16318/) (2023)
- [Breaking through the learning plateaus of in-context learning in Transformer](https://mlsanity.com/paper/2309.06054/) (2023)
- [Multilevel Initialization for Layer-Parallel Deep Neural Network Training](https://mlsanity.com/paper/1912.08974/) (2019)
- [Parallel Training of GRU Networks with a Multi-Grid Solver for Long Sequences](https://mlsanity.com/paper/2203.04738/) (2022)
- [The Impact of Noise on Evaluation Complexity: The Deterministic Trust-Region Case](https://mlsanity.com/paper/2104.02519/) (2021)
- [Design Guidelines for Noise-Tolerant Optimization with Applications in Robust Design](https://mlsanity.com/paper/2401.15007/) (2024)

## Built on by (most cited first, 2 of 2)

- [SNLP: Layer-Parallel Inference via Structured Newton Corrections](https://mlsanity.com/paper/2605.17842/) (2026)
- [An overview of machine learning-enhanced iterative methods for systems of linear and nonlinear equations](https://mlsanity.com/paper/2610.07211/) (2026)

## Abstract (arXiv)

We present a new training methodology for transformers using a multilevel, layer-parallel approach. Through a neural ODE formulation of transformers, our application of a multilevel parallel-in-time algorithm for the forward and backpropagation phases of training achieves parallel acceleration over the layer dimension. This dramatically enhances parallel scalability as the network depth increases, which is particularly useful for increasingly large foundational models. However, achieving this introduces errors that cause systematic bias in the gradients, which in turn reduces convergence when closer to the minima. We develop an algorithm to detect this critical transition and either switch to serial training or systematically increase the accuracy of layer-parallel training. Results, including BERT, GPT2, ViT, and machine translation architectures, demonstrate parallel-acceleration as well as accuracy commensurate with serial pre-training while fine-tuning is unaffected.